Two questions. What is "road"? And what does it mean that she can be called Tiffany?

Tshego is a child of southeast London. She has taught herself “road,” the slang emanating from the city’s grime music scene, but drops it the second she enters her apartment, a zone patrolled by her all-seeing South African mother. They squabble affectionately, for approximately the thousandth time, over whether she can be called Tiffany._________________Hiromichi

Nice to hear from you again! It happens I read the article you are referring to in your question. It appears that "Road" is the name of a slang used by people who enjoy "grime music". (I don't know what kind of music that is or what the slang is either, but I expect it is like rap slang used in the U.S.) There are many people who can switch from one dialect to a more standard dialect; for example, speaking one way in school and one way with friends. I would guess that Tshego, who is African and has an African name while living in England, is considering a name, "Tiffany" which would be more common in England.